\documentclass{standalone}

\usepackage{tikz}
\usepackage{graphene}

% rescale cells by
\def\rr{4}

\begin{document}
\begin{tikzpicture}
  %\graphene{(0,0)}{12}{12}
  \graphene{(-3,3*\sqrtTh)}{17}{16}

  \foreach \i in {0,...,3}{
    \draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(1.5*2*\i*\rr+3*\rr,\sqrtThOT*2*\i*\rr+\sqrtTh*\rr);
  }
  \foreach \i in {0,...,3}{
    \draw[line width=1pt, color=blue](0.5*\rr+3*\i*\rr,-3.5*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+12*\rr,-\sqrtThOT*2*\i*\rr+4*\sqrtTh*\rr);
  }

  \foreach \i in {0,...,3}{
    \draw[line width=1pt, color=blue](-1*\rr,-\i*\sqrtTh*\rr)--++(-1.5*2*\i*\rr+10.5*\rr,+\sqrtThOT*2*\i*\rr-3.5*\sqrtTh*\rr);
  }
  \foreach \i in {0,...,3}{
    \draw[line width=1pt, color=blue](-1*\rr+3*\i*\rr,\sqrtTh*\rr)--++(-1.5*2*\i*\rr+13.5*\rr,\sqrtThOT*2*\i*\rr-4.5*\sqrtTh*\rr);
  }
\end{tikzpicture}
\end{document}